There is a class of instruments that measures the coordinates of a point by sending a laser beam to a retroreflector target in contact with the point. The instrument determines the coordinates of the point by measuring the distance and the two angles to the target. The distance is measured with a distance-measuring device such as an ADM or an interferometer. The angles are measured with an angle-measuring device such as an angular encoder. A gimbaled beam-steering mechanism within the instrument directs the laser beam to the point of interest.
The laser tracker is a particular type of coordinate-measuring device that tracks the retroreflector target with one or more laser beams it emits. There is another category of instruments known as total stations or tachymeters that may measure a retroreflector or a point on a diffusely scattering surface. Laser trackers, which typically have accuracies on the order of a thousand of an inch and as good as one or two micrometers under certain circumstances, are usually much more accurate than total stations. The broad definition of laser tracker, which includes total stations, is used throughout this application.
Ordinarily the laser tracker sends a laser beam to a retroreflector target. A common type of retroreflector target is the SMR. In most cases, the term SMR is applied to a cube-corner retroreflector embedded within a metal sphere. However, the term SMR may also be applied to a cateye retroreflector embedded with a metal exterior spherical portion. Such a cateye retroreflector may be constructed in a shape of a sphere or in the shape of two adjoining hemispheres. A cube-corner retroreflector includes three mutually perpendicular reflectors. The vertex, which is the common point of intersection of the three reflectors, is located near the center of the sphere. In its normal tracking mode, the laser tracker sends a beam of light from the tracker to a position near the vertex of the SMR. As long as the beam of light strikes the vertex, the beam of returning beam of light retraces the path of the outgoing beam of light back to the tracker. If the beam of light strikes the SMR slightly off the vertex, the beam of light will return parallel to, but not exactly coincident with, the outgoing beam of light. A servo system within the tracker adjusts the direction of the beam emitted by the tracker to bring it back to the center, thereby allowing the beam to follow a moving retroreflector. Because the vertex is nearly coincident with the sphere center of the SMR, the perpendicular distance from the vertex to any surface on which the SMR rests remains nearly constant, even as the SMR is rotated. Consequently, the laser tracker can measure the 3D coordinates of a surface to a relatively high accuracy by following the position of an SMR as it is moved over the surface. Stating this another way, the laser tracker needs to measure only three degrees of freedom (one radial distance and two angles) to characterize the 3D coordinates of a surface.
An SMR may also be used to measure the distance between two nests. A particularly useful kind of nest is a kinematic nest, which has the property that an SMR can be repeatably positioned in the nest. One type of nest makes contact with the SMR surface at three points. Some types of nests are magnetic nests that hold the SMR securely in place against the nest contact points.
Some laser trackers have the ability to measure six degrees of freedom (DOF), which may include three translations, such as x, y, and z, and three rotations, such as pitch, roll, and yaw. An exemplary six-DOF laser tracker system is described in U.S. Pat. No. 7,800,758 ('758) to Bridges, et al., incorporated by reference herein. The '758 patent discloses a probe that holds a cube corner retroreflector, onto which marks have been placed. The cube corner retroreflector is illuminated by a laser beam from the laser tracker, and the marks on the cube corner retroreflector are captured by an orientation camera within the laser tracker. The three orientational degrees of freedom, for example, the pitch, roll, and yaw angles, are calculated based on the image obtained by the orientation camera. The laser tracker measures a distance and two angles to the vertex of the cube-corner retroreflector. When the distance and two angles, which give three translational degrees of freedom of the vertex, are combined with the three orientational degrees of freedom obtained from the orientation camera image, the position of a probe tip, arranged at a prescribed position relative to the vertex of the cube corner retroreflector, can be found. Such a probe tip may be used, for example, to measure the coordinates of a “hidden” feature that is out of the line of sight of the laser beam from the laser tracker.
As explained hereinabove, the vertex of a cube corner retroreflector within an SMR is ideally placed at the exact center of the sphere into which the cube corner is embedded. In practice, the position of the vertex is off the center of the sphere by up to a few thousandths of an inch. In some cases, the difference in the positions of the vertex and the sphere center are known to high accuracy, but this data is not used to correct the tracker readings. In the accurate measurements made with laser trackers, this error in the centering of the cube corner retroreflector in the sphere is sometimes larger than the errors from the distance and angle meters within the laser tracker. Consequently, there is a need for a method to correct this centering error.
Most of the SMRs in use today contain open-air cube corner retroreflectors. There are some SMRs that use glass cube corner retroreflectors, but in most cases these have limited accuracy. Because of the bending of the light entering such glass cube corners, the light appears to travel in a direction that is not the true direction within the cube corner. Consequently, SMRs made with glass cube corners tend to be made very small, as this reduces error, and they tend to be used in applications where the highest accuracy is not required. A method for minimizing this error using a six-DOF laser tracker is given in U.S. Pat. No. 8,467,072, the contents of which are incorporated by reference.
In many cases, the SMR of interest is an open-air cube corner rather than a glass cube corner, and the laser tracker measures only three degrees of freedom rather than six. Measurement error associated with such an SMR and tracker combination result both from errors in vertex centering and in sphere diameter. These errors can be corrected to an extent by purchasing a more expensive SMR having smaller centering and radius errors, but the errors cannot be eliminated. Furthermore, expensive SMRs are cost prohibitive in many applications. There is a need for a method to correct these errors, even for relatively inexpensive SMRs.